1. Field of the Invention
The present invention relates to modal analysis of a structure for determining dynamic vibratory characteristics thereof, and more particularly to modal analysis method and apparatus using acoustical excitation to impart vibration to the structure under test.
2. Brief Description of the Prior Art
Modal analysis techniques have been recently applied to many vibratory testing applications, and particularly in Environmental Stress Screening (ESS) tests such as those performed in printed circuit boards (PCB""s) manufacturing as part of quality control procedures.
According to conventional ESS procedures for testing PCB""s, determination of the vibration spectrum required for testing a particular PCB is usually an empirical matter. Induced fatigue and precipitation of latent defects are generally not estimated considering the actual stress within the circuit, but are rather empirically estimated from the vibration level as measured. Types of defects that are precipitated with a stimulation using random vibrations are mainly related to poor solders, component or substrate defects, connector problems, poor securing of cables and components, and structural problems. Methods of determining the spectrum of a vibrating excitation typically range from the study of vibrating behavior with comparison of the global response to predetermined optimum vibration levels, to the use of spectrums previously employed with success for other similar products. An intermediary method consists of introducing typical defects in a product and then increasing the vibration level until these defects repetitively precipitate, which method requires to apply long-continued vibrating stimulation, typically of about 10 minutes or more. In order to improve efficiency over these known methods, a structural model characterizing the vibration response of a product can be built prior to determine the spectrum of vibrating stimulation likely to produce the target frequency response profile. For this purpose, modal analysis techniques are used, such as those described in the applicants"" papers xe2x80x9cModal analysis of electronic circuit using acoustical sourcesxe2x80x9d, 4th Annual IEEE Accelerated Stress Testing, 1998, and xe2x80x9cExperimental modal analysis using acoustical sources (translated title)xe2x80x9d, 17th Canadian Congress on Applied Mechanics, 1999, which above reference present comparison results between some modal analysis techniques for the characterization of Printed Circuit Boards (PCB""s), namely hammer testing, shaker testing and acoustical excitation. Modal analysis essentially consists in establishing a theoretical model in terms of vibration parameters including resonance frequencies and damping factor associated with main modes of vibration. Then, values of these vibration parameters are determined experimentally using either a mechanical or acoustical source of vibration, such as disclosed in the inventor""s prior International PCT application no. WO 01/01103 to the applicants as published on Jan. 4, 2001, along with conventional vibration measuring instrumentation. From the obtained vibration parameters values, vibrating stimulation levels required to comply with ESS testing requirements can be predicted as well as optimal vibration spectrums. Acoustic excitation is a very attractive, non-contact approach for excitation of flexible structures. Unfortunately, an acoustical source does not produce a localized force on the structure under test, and therefore a plurality of vibration transducers (accelerometers) directly mounted on the article under test have been required heretofore, such as taught in the above-cited publications from the applicants. A complex set-up of transducers and cables must be realized to perform modal analysis of a specific structure to be tested, implying time-consuming calibration procedures.
It is therefore an object of the present invention to provide an acoustic-based modal analysis method and apparatus for determining dynamic vibration characteristics of a structure, which minimizes the number of output vibration transducers required.
According to a further broad aspect of the invention, there is provided a modal analysis method for acoustically determining dynamic vibration characteristics of a structure, the method comprising steps of: a) generating an acoustic excitation signal toward n spatially distributed locations associated with the structure while the latter is held to allow vibration thereof, one of said locations being a reference location; b) sensing the acoustic excitation signal at the locations to produce a corresponding set of n correlated input acoustic pressure-related electrical signals, one of the electrical signals being a reference signal associated with the reference location; c) converting the set of n correlated input acoustic pressure-related electrical signals into a set of correlated input acoustic pressure-related data in the frequency domain including reference data associated with the reference signal; d) sensing induced output vibration in response to the acoustic excitation at a reference point on the excited structure corresponding to the reference location to produce an output vibration response electrical signal; e) converting the output vibration response electrical signal into a set of output vibration response data in the frequency domain; f) providing n input transfer functions characterizing the correlation between the input acoustic pressure-related data and the reference data; g) performing said steps a) to f) for mxe2x88x921 complementary acoustic excitation signals with mxe2x89xa7n, to produce mxe2x88x921 complementary sets of input acoustic pressure-related data and to produce mxe2x88x921 complementary sets of output response vibration data; h) obtaining n structural transfer functions characterizing each set of input acoustic pressure-related data from relations between the m sets of n input transfer functions and the m sets of output vibration response data; and i) deriving from the structural transfer functions the dynamic vibratory characteristics of the structure.
According to a further broad aspect of the invention, there is provided a modal analysis method for acoustically determining dynamic vibration characteristics of a structure, the method comprising steps of: a) generating an acoustic excitation signal toward n spatially distributed locations associated with the structure while the latter is held to allow vibration thereof, one of said locations being a reference location; b) sensing the acoustic excitation signal at the locations to produce a corresponding set of n correlated input acoustic pressure-related electrical signals, one of the electrical signals being a reference signal associated with the reference location; c) converting the set of n correlated input acoustic pressure-related electrical signals into a set of correlated input acoustic pressure-related data in the frequency domain including reference data associated with the reference signal; d) sensing induced output vibration in response to the acoustic excitation at a reference point on the excited structure corresponding to the reference location to produce an output vibration response electrical signal; e) converting the output vibration response electrical signal into a set of output vibration response data in the frequency domain; f) providing n input transfer functions characterizing the correlation between the input acoustic pressure-related data and the reference data; g) performing said steps a) to f) for mxe2x88x921 complementary acoustic excitation signals with mxe2x89xa7n, to produce mxe2x88x921 complementary sets of input acoustic pressure-related data and to produce mxe2x88x921 complementary sets of output response vibration data; g) obtaining n structural transfer functions characterizing each set of input acoustic pressure-related data from relations between the m sets of n input transfer functions and the m sets of output vibration response data; and h) deriving from the structural transfer functions the dynamic vibratory characteristics of the structure.
According to a still further broad aspect of the invention, there is provided modal analysis apparatus for determining dynamic vibration characteristics of a structure. The apparatus comprises acoustical source means capable of generating m complementary sets of correlated acoustic excitation signals toward n spatially distributed locations associated with the structure, one of said locations being a reference location, and a structure holder provided with attachment means for holding the structure while allowing thereof to vibrate under the acoustic excitation signals. The apparatus further comprises acoustic sensor means responsive to the acoustic excitation signal at the locations to produce m complementary sets of n correlated input acoustic pressure-related electrical signals, one of the electrical signals being a reference signal associated with said reference location, and Fourier transform means for converting the sets of correlated input acoustic pressure-related electrical signals into sets of correlated input acoustic pressure-related data in the frequency domain including reference data associated with the reference signal. The apparatus further comprises vibration sensing means responsive to induced output vibration in response to the acoustic excitation at a reference point on the excited structure corresponding to the reference location to produce m complementary output vibration electrical signals and Fourier transform means for converting the output vibration electrical signals into m sets of output vibration data in the frequency domain. The apparatus further comprises data processor means responsive to the sets of correlated input acoustic pressure-related data and to the sets of output vibration data for providing n input transfer functions characterizing the correlation between each set of acoustic pressure-related data and the reference data, for obtaining n structural transfer functions characterizing each set of input acoustic pressure-related electrical data from relations between the m sets of n input transfer functions and the m sets of output vibration response data, and for deriving from the structural transfer functions the dynamic vibratory characteristics of the structure.